Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
/******************************************************************************

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Write your code in this editor and press "Run" button to execute it.

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import java.util.*;

public class Main
{
	public static void main (String [] args) {
	    int n;
	    Scanner scanner = new Scanner (System.in);
	    n = scanner.nextInt ();
	    if (n == 1) {
	        System.out.println ("1");
	        System.out.println ("1 1");
	    } else if (n == 2) {
	        System.out.println ("2");
	        System.out.println ("1 1");
	        System.out.println ("1 2");
	    } 
	    else {
	        Boolean toIncreaseM = false;
	        int m = 2;
	        for (int cn = 3; cn <= n; cn++) {
	            if (toIncreaseM) {
	                m++;
	                toIncreaseM = false;
	            } else {
	                toIncreaseM = true;
	            }
	        }
	        System.out.println (m);
	        int curRow = 1;
	        int curCol = 1;
	        Boolean toIncreaseRow = false;
	        for (int printedN = 0; printedN < n; printedN++) {
	            System.out.println (Integer.toString (curRow) + " " + Integer.toString (curCol));
	            if (toIncreaseRow) {
	                curRow++;
	                toIncreaseRow = false;
	            } else {
	                curCol++;
	                toIncreaseRow = true;
	            }
	        }
	    }
	}
}